Question Paper Code: 8·4558

B.E.lB.Tech. DEGREE EXAMINATION, NOVEMBERJDECEMBER 2009.

Fourth Semester

Mechanical Engineering

(Common to Second Semester Mechatronics Engineering)

CE 251- STRENGTH OF MATERIALS

(Regulation 2001)

Time: Three hours Maximum: 100 marks

Answer ALL questions.

PART A- (10 x 2 = 20 marks)

1. Derive a relation for change in length of a bar hanging freely under its ownweight.

2. A brass rod 2 m long is fixed at both its ends. If the thermal stress is not toexceed 76.5 N/mm2. Calculate the temperature through which the rod shouldbe heated. Take the values of a and E as 17 x 10-6/K and 90 GPa respectively.

3. Draw shear force diagram for a simply supported beam of 5 m span issubjected to a clockwise moment of 15 kN.m at a distance of 2 m from the leftend.

4. Sketch the bending and shear stress distribution for a 'T' section.

5. Show that the shear stress distribution over a rectangular section is parabolic.

6. Calculate the maximum torque that a shaft of 125 mm diameter can transmit,if the maximum angle of' twist is 1° in a length of 1.5 m. TakeC = 70 X 103 Nzmm-,

7. A cylindrical shell of 500 mm diameter is required to withstand an internalpressure of 4 MPa. Find the minimum thickness of the shell, if maximumtensile strength in the plate material is 400 N/mm2 and efficiency of joint is65%. Take factor of safety as 5.

8. A rectangular R.C simply supported beam of span 3 m and cross section200 mm x 350 mm carries a point load of 100 kN at its mid span. Find themaximum slope and deflection of the beam if E = 0.2 X 105 Nzmm-.

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9. Draw conjugate beam for a cantilever carrying uniformly distributed load overthe entire span.

10. Define strain energy density.

PART B - (5 x 16 = 80 marks)

11. (a) (i) State Moment - Area Mohr's theorems. (4)

(ii) A simply supported beam AB of uniform section, 4 m span issubjected to a clockwise moment of 10 KN.m applied at the righthinge B. Derive the equation to the deflected shape of the beam.Locate the point of maximum deflection and find the maximumdeflection. (12)

2 S 4558

Or

(b) (i) Derive a relation for change in length of a bar of uniformly taperingcircular section subjected to an axial tensile load 'W'. (8)

(ii) A reinforced concrete column 500 mm x 500 mm in section isreinforced with 4 steel bars of 25 mm diameter, one in each corner,the column is carrying a load of 1000 KN. Find the stresses in theconcrete and steel bars. Take E for steel = 210 x 103 N/mm2 and Efor concrete = 14 x 103 N/mm2. (8)

12. (a) Draw the shear force and bending moment diagram for the beam shownin Figure 12 (a) and also locate the point of contratlexure.

Figure 12 (a)

Or

(b) A simply supported beam AB of span 5 m carries a UDL of 25 KN/mthroughout its entire span. Calculate the deflection at its mid span usingany method. Assume EI = 2 x 104 KNm2.

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13. (a) A solid shaft is subjected to a torque of 100 Nm. Find the necessary shaftdiameter if the allowable shear stress is 100 N/mm2 and the allowabletwist is 30 per 10 diameter length of the shaft. Take C = 1 X 105 N/mm2.

Or

(b) (i) State any four assumptions made in the theory of simple bending.(4)

(ii) Derive the bending formula (12)

M f E-=-=-I y R

14. (a) A thin cylindrical shell 1.5 m long, internal diameter 300 mm and wallthickness 10 mm is filled up with a fluid at atmospheric pressure. If theadditional fluid of 300 x 103 mm" is pumped in the shell, find thepressure exerted by the fluid on the shell. Take E= 2 x 105 N/mm2 and11m= 0.3. Also find the hoop stress induced.

Or

(b) (i) Derive a relation for deflection of a closely coiled helical springsubjected to an axial downward load W. (8)

(ii) A quarter elliptic leaf spring 60 em long is made of steel plates ofwidth 10 times the thickness. The spring is to carry a load of 3 KNand the end deflection is limited to 5 em. The bending stress of theplates must not exceed 3000 Nzmm>, Find suitable values of the sizeand number of plates to be used. Take E = 2 X 105 Nzmm". (8)

15. (a) A cantilever of length 2 a is carrying a load of W at the free end, andanother load of W at its centre. Determine by moment area method, theslope and deflection of the cantilever at the free end.

Or .

(b) (i) Derive a relation for strain energy stored in a body due to shearstress. (6) .

(ii) A rectangular body 500 mm long, 100 mm wide and 50 mm thick issubjected to a shear stress of 80 Mpa. Determine the strain energystored in the body. Take N = 85 X 103 N/mm2. (10)

3 S 4558

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